Boundary Value Problems

Author: F. D. Gakhov
Publisher: Elsevier
ISBN: 1483164985
Format: PDF, ePub, Mobi
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Boundary Value Problems is a translation from the Russian of lectures given at Kazan and Rostov Universities, dealing with the theory of boundary value problems for analytic functions. The emphasis of the book is on the solution of singular integral equations with Cauchy and Hilbert kernels. Although the book treats the theory of boundary value problems, emphasis is on linear problems with one unknown function. The definition of the Cauchy type integral, examples, limiting values, behavior, and its principal value are explained. The Riemann boundary value problem is emphasized in considering the theory of boundary value problems of analytic functions. The book then analyzes the application of the Riemann boundary value problem as applied to singular integral equations with Cauchy kernel. A second fundamental boundary value problem of analytic functions is the Hilbert problem with a Hilbert kernel; the application of the Hilbert problem is also evaluated. The use of Sokhotski's formulas for certain integral analysis is explained and equations with logarithmic kernels and kernels with a weak power singularity are solved. The chapters in the book all end with some historical briefs, to give a background of the problem(s) discussed. The book will be very valuable to mathematicians, students, and professors in advanced mathematics and geometrical functions.

Boundary Value Problems

Author: Chi Yeung Lo
Publisher: World Scientific
ISBN: 9789810243005
Format: PDF
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This book has been designed for a one-year graduate course on boundary value problems for students of mathematics, engineering, and the physical sciences. It deals mainly with the three fundamental equations of mathematical physics, namely the heat equation, the wave equation, and Laplace's equation. The goal of the book is to obtain a formal solution to a given problem either by the method of separation of variables or by the method of general solutions and to verify that the formal solution possesses all the required properties. To provide the mathematical justification for this approach, the theory of Sturm-Liouville problems, the Fourier series, and the Fourier transform are fully developed. The book assumes a knowledge of advanced calculus and elementary differential equations.

Boundary Value Problems for Partial Differential Equations and Applications in Electrodynamics

Author: N. E. Tovmasyan
Publisher: World Scientific
ISBN: 9789810213510
Format: PDF, Kindle
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The book is devoted to boundary value problems for general partial differential equations. Efficient methods of resolution of boundary value problems for elliptic equations, based on the theory of analytic functions and having great theoretical and practical importance are developed.A new approach to the investigation of electromagnetic fields is sketched, permitting laws of propagation of electromagnetic energy at a great distance, is outlined and asymptotic formulae for solutions of Maxwell's equation is obtained. These equations are also applied to the efficient resolution of problems.The book is based mostly on the investigation of the author, a considerable part of which being published for the first time.

Mixed Boundary Value Problems

Author: Dean G. Duffy
Publisher: CRC Press
ISBN: 9781420010947
Format: PDF, ePub
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Methods for Solving Mixed Boundary Value Problems An up-to-date treatment of the subject, Mixed Boundary Value Problems focuses on boundary value problems when the boundary condition changes along a particular boundary. The book often employs numerical methods to solve mixed boundary value problems and the associated integral equations. Straightforward Presentation of Mathematical Techniques The author first provides examples of mixed boundary value problems and the mathematical background of integral functions and special functions. He then presents classic mathematical physics problems to explain the origin of mixed boundary value problems and the mathematical techniques that were developed to handle them. The remaining chapters solve various mixed boundary value problems using separation of variables, transform methods, the Wiener–Hopf technique, Green’s function, and conformal mapping. Decipher Mixed Boundary Value Problems That Occur in Diverse Fields Including MATLAB® to help with problem solving, this book provides the mathematical skills needed for the solution of mixed boundary value problems.

Boundary Value Problems

Author: David L. Powers
Publisher: Academic Press
ISBN: 0080884415
Format: PDF, Mobi
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Boundary Value Problems, Sixth Edition, is the leading text on boundary value problems and Fourier series for professionals and students in engineering, science, and mathematics who work with partial differential equations. In this updated edition, author David Powers provides a thorough overview of solving boundary value problems involving partial differential equations by the methods of separation of variables. Additional techniques used include Laplace transform and numerical methods. The book contains nearly 900 exercises ranging in difficulty from basic drills to advanced problem-solving exercises. Professors and students agree that Powers is a master at creating examples and exercises that skillfully illustrate the techniques used to solve science and engineering problems. Ancillary list: Online SSM- http://www.elsevierdirect.com/product.jsp?isbn=9780123747198 Online ISM- http://textbooks.elsevier.com/web/manuals.aspx?isbn=9780123747198 Companion site, Ebook- http://www.elsevierdirect.com/companion.jsp?ISBN=9780123747198 Student Solution Manual for Sixth Edition - https://www.elsevier.com/books/student-solutions-manual-boundary-value-problems/powers/978-0-12-375664-0 New animations and graphics of solutions, additional exercises and chapter review questions on the web Nearly 900 exercises ranging in difficulty from basic drills to advanced problem-solving exercises Many exercises based on current engineering applications

A Unified Approach to Boundary Value Problems

Author: Athanassios S. Fokas
Publisher: SIAM
ISBN: 0898716519
Format: PDF, Mobi
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A novel approach to analysing initial-boundary value problems for integrable partial differential equations (PDEs) in two dimensions, based on ideas of the inverse scattering transform that the author introduced in 1997. This method is unique in also yielding novel integral representations for linear PDEs. Several new developments are addressed in the book, including a new transform method for linear evolution equations on the half-line and on the finite interval; analytical inversion of certain integrals such as the attenuated Radon transform and the Dirichlet-to-Neumann map for a moving boundary; integral representations for linear boundary value problems; analytical and numerical methods for elliptic PDEs in a convex polygon; and integrable nonlinear PDEs. An epilogue provides a list of problems on which the author's new approach has been used, offers open problems, and gives a glimpse into how the method might be applied to problems in three dimensions.

An Introduction to Nonlinear Boundary Value Problems

Author: Lakshmikantham
Publisher: Academic Press
ISBN: 0080956181
Format: PDF, ePub, Mobi
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A book on an advanced level that exposes the reader to the fascinating field of differential equations and provides a ready access to an up-to-date state of this art is of immense value. This book presents a variety of techniques that are employed in the theory of nonlinear boundary value problems. For example, the following are discussed: methods that involve differential inequalities; shooting and angular function techniques; functional analytic approaches; topological methods.

Initial Boundary Value Problems and the Navier Stokes Equation

Author: Heinz-Otto Kreiss
Publisher: SIAM
ISBN: 0898715652
Format: PDF, ePub, Mobi
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Initial-Boundary Value Problems and the Navier-Stokes Equations gives an introduction to the vast subject of initial and initial-boundary value problems for PDEs. Applications to parabolic and hyperbolic systems are emphasized in this text. The Navier-Stokes equations for compressible and incompressible flows are taken as an example to illustrate the results. The subjects addressed in the book, such as the well-posedness of initial-boundary value problems, are of frequent interest when PDEs are used in modeling or when they are solved numerically. The book explains the principles of these subjects. The reader will learn what well-posedness or ill-posedness means and how it can be demonstrated for concrete problems. Audience: when the book was written, the main intent was to write a text on initial-boundary value problems that was accessible to a rather wide audience. Functional analytical prerequisites were kept to a minimum or were developed in the book. Boundary conditions are analyzed without first proving trace theorems, and similar simplifications have been used throughout. This book continues to be useful to researchers and graduate students in applied mathematics and engineering.